Shortest line on solid

There is a solid OABC surrounded with the four sheets of the equilateral triangle whose length of one side is 10 cm.

The point of the middle of the side AC is set to M and the points P and Q are on the sides OB and OC, respectively.

As shown in a figure, the straight line AP, PQ, and QM are drawn.

Find the ratio of AP : PQ : QM in case that the sum of the length of the straight line AP, PQ, and QM becomes the minimum.

Answer